cp's OEIS Frontend

A306854 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct Fermi-Dirac prime factors.

%I A306854 #14 Mar 16 2019 16:13:07
%S A306854 1,840,3,280,9,120,7,216,5,168,11,210,4,270,13,264,15,56,27,40,21,72,
%T A306854 33,70,12,90,28,30,36,42,20,54,35,24,45,66,52,96,44,78,55,84,10,108,
%U A306854 14,60,18,105,8,135,22,140,6,180,26,132,32,156,34,165,38,189,46
%N A306854 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 5 distinct Fermi-Dirac prime factors.
%C A306854 This sequence is a variant of A285487. Both sequences are permutations of the natural numbers and have similar graphical features.
%H A306854 Rémy Sigrist, <a href="/A306854/b306854.txt">Table of n, a(n) for n = 1..10000</a>
%H A306854 OEIS Wiki, <a href="/wiki/%22Fermi-Dirac_representation%22_of_n">"Fermi-Dirac representation" of n</a>
%H A306854 Rémy Sigrist, <a href="/A306854/a306854.png">Colored scatterplot of the first 10000 terms</a> (where the color is function of A064547(a(n)))
%H A306854 Rémy Sigrist, <a href="/A306854/a306854.gp.txt">PARI program for A306854</a>
%H A306854 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A306854 A064547(a(n) * a(n+1)) >= 5.
%e A306854 The first terms, alongside the Fermi-Dirac factorization of a(n) * a(n+1), are:
%e A306854   n   a(n)  a(n) * a(n+1)
%e A306854   --  ----  -------------
%e A306854    1     1  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
%e A306854    2   840  2^(2^0) * 2^(2^1) * 3^(2^1) * 5^(2^0)  * 7^(2^0)
%e A306854    3     3  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
%e A306854    4   280  2^(2^0) * 2^(2^1) * 3^(2^1) * 5^(2^0)  * 7^(2^0)
%e A306854    5     9  2^(2^0) * 2^(2^1) * 3^(2^0) * 3^(2^1)  * 5^(2^0)
%e A306854    6   120  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
%e A306854    7     7  2^(2^0) * 2^(2^1) * 3^(2^0) * 3^(2^1)  * 7^(2^0)
%e A306854    8   216  2^(2^0) * 2^(2^1) * 3^(2^0) * 3^(2^1)  * 5^(2^0)
%e A306854    9     5  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
%e A306854   10   168  2^(2^0) * 2^(2^1) * 3^(2^0) * 7^(2^0)  * 11^(2^0)
%e A306854   11    11  2^(2^0) * 3^(2^0) * 5^(2^0) * 7^(2^0)  * 11^(2^0)
%e A306854   12   210  2^(2^0) * 2^(2^1) * 3^(2^0) * 5^(2^0)  * 7^(2^0)
%o A306854 (PARI) See Links section.
%Y A306854 Cf. A064547, A285487, A306856 (inverse).
%K A306854 nonn,look
%O A306854 1,2
%A A306854 _Rémy Sigrist_, Mar 13 2019